A numerical technique based on collocation method for solving modified Kawahara equation

Abstract

In this article, a numerical solution of the modified Kawahara equation is presented by septic B-spline collocation method. Applying the von-Neumann stability analysis, the present method is shown to be unconditionally stable. L 2 and L ∞ error norms and conserved quantities are given at selected times. The accuracy of the proposed method is checked by test problems including motion of the single solitary wave, interaction of solitary waves and evolution of solitons.